Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Closed mappings and quasimetrics


Author: Jacob Kofner
Journal: Proc. Amer. Math. Soc. 80 (1980), 333-336
MSC: Primary 54E15; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1980-0577769-6
MathSciNet review: 577769
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Closed continuous mappings with first countable images preserve quasi-metric spaces as well as nonarchimedean quasi-metric spaces and $ \gamma $-spaces. This is a strict generalization of analogous results on perfect mappings: there exists a closed continuous mapping of a nonarchimedean quasi-metric Moore space onto a compact metric space which is neither perfect nor boundary compact.

References [Enhancements On Off] (What's this?)

  • [B] H. R. Bennett, Quasi-metrizability and the $ \gamma $-space property in certain generalized metric spaces, Topology Proceedings 4 (1979), 1-13. MR 583684 (81m:54063)
  • [F] R. Fox, On metrizability and quasi-metrizability (to appear).
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag, Berlin and New York, 1976. MR 0407579 (53:11352)
  • [G] G. Gruenhage, A note on quasi-metrizability, Canad. J. Math. 29 (1977), 360-366. MR 0436089 (55:9040)
  • [J1] H. Junnila, Covering properties and quasi-uniformities of topological spaces, Ph. D. Thesis, Virginia Polytechnic Institute and State University, 1978.
  • [J2] -, Neighbornets, Pacific J. Math. 76 (1978), 83-108. MR 0482677 (58:2734)
  • [K1] J. Kofner, On $ \Delta $-metrizable spaces, Mat. Zametki 13 (1973), 277-287 = Math. Notes 13 (1973), 168-170. MR 0324664 (48:3014)
  • [K2] -, Semi-stratifiable spaces and spaces with generalized metrices, Ph. D. Thesis, The Technion, Haifa, Israel, 1975.
  • [K3] -, Quasi-metrizable spaces, Pacific J. Math. 82 (1979).
  • [NC] S. Nedev and M. Čoban, On the theory of o-metrizable spaces. III, Vestnik Moskov. Univ. Ser. I. Mat. Meh. 27 (1972), 10-15. (Russian) MR 0307192 (46:6312)
  • [TP] Topology Proceedings 2 (1977), 687.
  • [V] N. V. Velicko, Quasi-uniformly sequential spaces, C. R. Acad. Bulgare Sci. 25 (1972), 589-591. (Russian) MR 0305324 (46:4454)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E15, 54C10

Retrieve articles in all journals with MSC: 54E15, 54C10

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577769-6
Keywords: Closed mapping, quasi-metric, nonarchimedean quasi-metric, $ \gamma $-space, perfect mapping, first countable space
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society